Calculating average joint hamming weight for minimal weight conversion of d integers

Vorapong Suppakitpaisarn*, Masato Edahiro, Hiroshi Imai

*この研究の対応する著者

研究成果: Conference contribution

抄録

In this paper, we propose an algorithm to calculate the efficiency of number representations in elliptic curve cryptography, average joint Hamming weight. The method uses Markov chains generated from a minimal weight conversion algorithm of d integers using the minimal weight conversion. With redundant representations using digit sets like {0, ±1}, it is possible to reduce computation time of the cryptosystem. Although larger digit sets make the computation time shorter, it requires longer preprocessing time. Therefore, the average joint Hamming weight is useful to evaluate digit sets. The Markov chains to find the average joint Hamming weight are derived automatically from the conversions. However, the number of states in these Markov chains is generally infinite. In [8], we propose an algorithm to reduce the number of states, but it is still unclear which representations the method can be applied for. In this paper, the finiteness of Markov chain with the existence of a stationary distribution is proven in a class of representation whose digit set D S be a finite set such that there exists a natural number Λ where D S ⊆ {0, ±1, ..., ±Λ} and {0,±1, ±Λ} ⊆ D S. The class covers most of the representation practically used in elliptic curve cryptography such as the representation which digit set are {0, ±1} and {0, ±1, ±3}.

本文言語English
ホスト出版物のタイトルWALCOM
ホスト出版物のサブタイトルAlgorithms and Computation - 6th International Workshop, WALCOM 2012, Proceedings
ページ229-240
ページ数12
DOI
出版ステータスPublished - 2012
イベント6th International Workshop on Algorithms and Computation, WALCOM 2012 - Dhaka, Bangladesh
継続期間: 2012 2 152012 2 17

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
7157 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Conference

Conference6th International Workshop on Algorithms and Computation, WALCOM 2012
国/地域Bangladesh
CityDhaka
Period12/2/1512/2/17

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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